Understanding the molecular mechanism in a regiospecific [3 + 2] cycloaddition reaction including C–O and C–S interactions: an ELF topological analysis

Abstract

A theoretical study at the MPWB1K/6-311G(d) level was performed on the [3 + 2] cycloaddition (32CA) reaction of (Z)-2,2,2-trifluoro-N-methylethan-1-imine oxide (nitrone 10) toward propane-2-thione (thioketone 11) as a reduced computational model considered for experimentally studied 32CA reaction between (Z)-2,2,2-trifluoro-N-phenylethan-1-imine oxide (nitrone 6a) and 2,4-dimethylpentane-3-thione (thioketone 8f). Exploration of relative Gibbs free energy profile in the presence of THF obviously showed that among two feasible meta and ortho regioisomeric channels, the former is completely preferred over the latter both kinetically, ΔΔG_activation = 11.1 kcal mol⁻¹, and thermodynamically, ΔΔG_reaction = −16.1 kcal mol⁻¹. The energetic results of the modelled reaction, in complete agreement with the experimentally studied reaction, emphasize that the meta cycloadduct is the unique observable formal [3 + 2] yield. The moderate global nucleophilicity and electrophilicity characters found in nitrone 10 and thioketone 11, respectively, are responsible for a very low polar character of the studied 32CA reaction. The complete regioselectivity in the modelled 32CA reaction can be explained using calculated electrophilic and nucleophilic Parr functions at the interacting sites of reagents. The ELF topological patterns indicate that in the 32CA reaction between nitrone 10 and thioketone 11 while the formation of a C–S single bond at one terminal takes place exactly according to the recently proposed Domingo's model, formation of an O–C single bond at the other terminal is a direct consequence of donation of some electron density of oxygen lone pairs of nitrone 10 to the carbon atom of thioketone 11.

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1. Introduction

Five-membered heterocyclic compounds can widely be prepared via a general and extensively applicable route, namely [3 + 2] cycloaddition (32CA) reactions.¹ A 32CA reaction will make sense when a three-atom-component (TAC) reacts with an unsaturated bond to generate a five-membered heterocycle yield. Traditionally, most of chemists name this kind of cycloaddition reactions as “1,3-dipolar” ones to demonstrate involvement of “1,3-dipole” species in the reaction toward unsaturated bonds via a pericyclic concerted mechanism. Nevertheless, using “TAC” and “[3 + 2]” terms instead of “1,3-dipole” and “1,3-dipolar” phrases, respectively, are conceptually more capable to describe the nature of these reactions and electronic behaviour of the involved species.^2,3

The electronic nature of the TACs involved in [3 + 2] cycloaddition reactions allows these reactions to be classified into pseudodiradical-type (pr-type) reactions involving TACs with a high pseudodiradical character, e.g. carbonyl ylides, which take place easily through an early transition state (TS) with non-polar character, and zwitterionic-type (zw-type) reactions involving TACs with a high zwitterionic character; e.g., nitrile oxides, characterized by favourable nucleophilic/electrophilic interactions, taking place through polar TSs.^2–7

Nitrones (azomethine N-oxides) are a well-known class of TACs which undergo 32CA reaction toward C=C, C≡C, and C=N multiple bonds as a very popular synthetic utility allowing a rapid construction of five-membered heterocycles with some distinguished biological activities.^8,9 The very high reactivity of C=S double bond of thioketones in 32CA reactions toward thiocarbonyl ylides, diazoalkanes, and nitrones has been turned out. For instant, adamantanethione 2a, despite steric hindrance, reacts 1500 times faster than dimethyl acetylenedicarboxylate 2b at 25 °C in 32CA reaction toward N-methyl-C-phenylnitrone 1¹⁰ (see Scheme 1).

Scheme 1 32CA reaction of N-methyl-C-phenylnitrone 1 with adamantanethione 2a and dimethyl acetylenedicarboxylate 2b.¹⁰

In addition, a theoretical study has been performed on the 32CA reaction of simplest nitrone, methanimine oxide 3, toward thioformaldehyde 4 and ethylene 5 according to three ab initio procedures.¹¹ MP2/6-31G(d) relative energy profile associated with these 32CA reactions is schematically depicted in Scheme 2.

Scheme 2 A schematic representation of MP2/6-31G(d) relative total electronic energy including zero point vibrational energy, ZPVE, correction for 32CA reaction of simplest nitrone 3 toward thioformaldehyde 4 (left) and ethylene 5 (right).¹¹

As shown in Scheme 2, while TS1 is located just 0.2 kcal mol⁻¹ over orientation complex, TS2 is found 12.0 kcal mol⁻¹ above corresponding orientation complex indicating more reactivity of C=S double bond than C=C one in 32CA reaction toward nitrone 3.

While nitrones bearing fluorine substitutions provide potential application to synthesis of fluorinated heterocycles, they have received lesser attention than other nitrones. Participation of mentioned nitrones in a 32CA reaction toward C=S double bond, which are rarely followed, can produce fluorinated five-membered cycloadducts including three N, O, and S hetero atoms. Such cycloadducts, due to presence of fluorine substitutions are noticeably stable enabling synthetic interests as target molecules and even building blocks to generate more complex compounds.¹² Very recently, a set of complete regioselective 32CA reactions of fluorinated nitrones 6a and 7b toward various thioketones 8a-g in the presence of tetrahydrofuran (THF) furnishing cycloadducts 9a-i have experimentally been studied by Mlostoń and co-workers (see Scheme 3).¹²

Scheme 3 32CA reactions of fluorinated nitrones 6a and 7b toward thioketones 8a–g experimentally studied by Mlostoń and co-workers.¹²

Herein, in line with experimental work of Mlostoń and co-workers, a density functional theory (DFT) study on the 32CA reaction between nitrone 10 and thioketone 11 is performed at the MPWB1K/6-311G(d) level in order to characterize the energetic, complete regioselectivity, and the reaction mechanism of this process. Moreover, an electron localization function (ELF)^13–16 topological analysis of the most relevant points along the intrinsic reaction coordinate (IRC)¹⁷ curve of the 32CA reaction between nitrone 10 and thioketone 11 is carried out in order to characterise the bonding changes along the studied 32CA reaction and, thus, to establish the molecular mechanism of this reaction in detail. The ELF study can exhibit interesting mechanistic patterns for 32CA reaction between nitrone 10 and thioketone 11 in which carbon-heteroatoms, C–O and C–S, interactions lead to generate corresponding cycloadduct.

It is worth noting that in order to build a reduced computational model such that becomes easier to study, in one hand, and also does not produce significant changes compared to what experimentally considered, on the other hand, nitrone 10 and thioketone 11 were generated by replacement of Bn (benzyl) substitution with methyl group in nitrone 6a and i-Pr (isopropyl) substitutions with methyl ones in thioketone 8f, respectively (see Scheme 4).

Scheme 4 Reaction paths involved in the 32CA reaction of nitrone 10 toward thioketone 11 as a reduced computational model for 32CA reaction of nitrone 6a with thioketone 8f experimentally studied by Mlostoń and co-workers.¹²

2. Computational details

Recently, Truhlar's group have shown that the MPWB1K hybrid meta density functional method (HMDFT) gives good results for thermochemistry and thermochemical kinetics as well as excellent saddle point geometries.¹⁸ Consequently, in the present study, DFT computations were carried out using the MPWB1K exchange-correlation functional, together with the standard 6-311G(d) basis set.¹⁹ Berny analytical gradient optimization method using GEDIIS²⁰ was employed in geometry optimization steps. The stationary points were characterized by frequency calculations in order to verify that TSs have one and only one imaginary frequency. The IRC paths¹⁷ were traced in order to check the energy profiles connecting each TS to the two associated minima of the proposed mechanism using the Hessian-based Predictor-Corrector (HPC) integrator algorithm.²¹ Solvent effects of THF (ε = 7.42) were taken into account in the optimizations using the polarizable continuum model (PCM) as developed by Tomasi's group²² in the framework of the self-consistent reaction field (SCRF).²³ Values of enthalpies, entropies, and Gibbs free energies in the gas phase as well as in the presence of THF were calculated with standard statistical thermodynamics at 298 K and 1 atm.¹⁹ The electronic structures of stationary points were analysed by the natural bond orbital (NBO) method.²⁴ The ELF study was performed with the TopMod program²⁵ using the corresponding monodeterminantal wave functions of the selected structures along the IRC curve. All computations were carried out with the Gaussian 09 suite of programs.²⁶

The global electrophilicity index ω²⁷ is given by the following expression, ω = μ²/2η based on the electronic chemical potential, μ, and the chemical hardness, η. Both quantities may be approached in terms of the one-electron energies of the frontier molecular orbital HOMO and LUMO, ε_H and ε_L, as μ ≈ (ε_H + ε_L)/2 and η ≈ (ε_L − ε_H), respectively.²⁸ The global nucleophilicity index N,²⁹ based on the HOMO energies obtained within the Kohn–Sham scheme,³⁰ is defined as N = ε_HOMO (Nu) − ε_HOMO (TCE) in which (Nu) denotes the given nucleophile. This relative nucleophilicity index refers to tetracyanoethylene (TCE). Nucleophilic P_k⁻ and electrophilic P_k⁺ Parr functions³¹ were obtained through the analysis of the Mulliken atomic spin density (ASD) of the radical cation of nitrone 10 and the radical anion of thioketone 11, respectively. The local electrophilicity index, ω_k, and local nucleophilicity index, N_k, were calculated using ω_k = ωP_k⁺ and N_k = NP_k⁻ relationships.⁷

3. Results and discussion

The present study is divided into three parts: (i) first, as presented in Scheme 4, the reaction paths involved in the computationally modelled 32CA reaction of nitrone 10 with thioketone 11 yielding corresponding regioisomeric cycloadducts CAo and CAm are studied; (ii) in the second part, an analysis of the global and local DFT reactivity indices of the reagents involved in the considered 32CA reaction is performed in order to explain reactivity and regioselectivity in the cycloaddition between nitrone 10 and thioketone 11; (iii) finally, in the third part, an ELF topological analysis along 32CA reaction of nitrone 10 toward thioketone 11 is carried out in order to characterize the molecular mechanism in this cycloaddition.

3.1. Study of the reaction paths involved in the 32CA reaction of nitrone 10 with thioketone 11

Due to the asymmetry of both reagents, two competitive reactive channels are feasible for the 32CA reaction between nitrone 10 and thioketone 11. They are related to the two regioisomeric approach modes of the C1 carbon atom of nitrone 10 toward the C4 carbon (via ortho channel) or S5 (via meta channel) sulfur atoms of thioketone 11 (see Scheme 4 for atoms numbering). Ortho and meta channels naming is an arbitrary consideration to indicate relative position of oxygen and sulfur atoms in the mentioned regioisomeric pathways. It is worth noting that stereoisomeric approach modes, exo and endo, are meaningless because of the axial symmetry in thioketone 11. An analysis of stationary points involved in the two regioisomeric paths indicates that this 32CA reaction takes place through a one-step mechanism. On the other hand, the formation of a reactive pre-complex between reagents has been proved in the case of some 32CA reactions.^6,32,33 Consequently, two reactive pre-complexes, RPCm and RPCo, two TSs, TSm and TSo, and two corresponding formal [3 + 2] cycloadducts, CAm and CAo, were located and characterized on the potential energy surface (PES) of this reaction. It is interesting to mention that RPCs can structurally be found at the first point of the corresponding IRC curve toward TS.³ Note that “m” and “o” abbreviations denote meta and ortho, respectively. Thermochemical parameters calculated for the 32CA reaction of nitrone 10 toward thioketone 11 in the gas phase as well as in the presence of THF are displayed in Table 1. As displayed in Table 1, when two reagents gradually approach each other, the two reactive pre-complexes are allowed to form due to reduce of enthalpy by 5.8 and 1.8 kcal mol⁻¹ in the case of RPCm and RPCo, respectively. Because of the bimolecular nature of reaction, as shown in the fourth column of Table 1, the entropies shift into highly negative values along approaching reagents acting as an unfavourable factor in the thermodynamic stability of RPCm and RPCo.

Table 1 MPWB1K/6-311G(d) thermochemical parameters for the 32CA reaction of nitrone 10 toward thioketone 11 in the gas phase as well as in the presence of THF

	Transition	ΔH (kcal mol^−1)	ΔS (cal mol^−1 K^−1)	ΔG (kcal mol^−1)
Gas phase (ε = 1.00)	Nitrone10 + thioketone11 → RPCm	−5.8	−46.0	7.9
	Nitrone10 + thioketone11 → TSm	1.9	−52.8	17.7
	Nitrone10 + thioketone11 → CAm	−34.9	−55.5	−18.3
	Nitrone10 + thioketone11 → RPCo	−1.8	−46.5	12.5
	Nitrone10 + thioketone11 → TSo	13.1	−55.2	29.6
	Nitrone10 + thioketone11 → CAo	−19.2	−58.6	−1.7
THF (ε = 7.42)	Nitrone10 + thioketone11 → RPCm	−3.3	−41.0	8.9
	Nitrone10 + thioketone11 → TSm	4.7	−49.7	19.5
	Nitrone10 + thioketone11 → CAm	−29.1	−53.5	−13.2
	Nitrone10 + thioketone11 → RPCo	−0.6	−43.6	12.4
	Nitrone10 + thioketone11 → TSo	14.9	−52.7	30.6
	Nitrone10 + thioketone11 → CAo	−13.8	−56.1	2.9

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In other word, when the unfavourable entropy term, TΔS, is summed to the corresponding enthalpy changes a significant increase is produced in the corresponding Gibbs free energies, 7.9 kcal mol⁻¹ (RPCm) and 12.5 kcal mol⁻¹ (RPCo), ruling out the presence of RPCs as the stable species at the room temperature. Further approach of regents leads to the formation of TSs which are enthalpically located 1.9 (TSm) and 13.1 (TSo) kcal mol⁻¹ over the separate reagents or 7.7 and 14.9 kcal mol⁻¹ over RPCm and RPCo, respectively. These values clearly indicate that meta regioisomeric pathway is the unique channel which can kinetically be reached. On the other hand, the gas phase reaction enthalpies corresponded to regioisomeric cycloadducts are −34.9 (CAm) and −19.2 (CAo) kcal mol⁻¹ demonstrating the high exothermic nature of studied 32CA reaction particularly in the reachable meta channel. Because of the noticeable contribution of unfavourable TΔS term, the gas phase activation and reaction Gibbs free energies associated with the more favourable meta channel become 17.7 (TSm) and −18.3 (CAm) kcal mol⁻¹ displaying a noteworthy rise compared with the corresponding enthalpy values. Relative Gibbs free energies perceptibly imply that 32CA reaction between nitrone 10 and thioketone 11 in the gas phase takes place via a strongly regioselective (regiospecific) fashion passing through TSm (ΔΔG_activation = 11.9 kcal mol⁻¹) yielding CAm (ΔΔG_reaction = −16.6 kcal mol⁻¹) as the unique kinetically and thermodynamically reachable cycloadduct.

When solvent effects of THF are taken into account not only RPCs are not thermodynamically allowed to form but also formation of unfavourable CAo becomes completely nonspontaneous (ΔG = 2.9 kcal mol⁻¹) and the exergonic character of reaction clearly decreases in the more favourable meta channel due to more solvation of reagents than CAm. The relative thermochemical parameters (ΔH, TΔS, and ΔG) associated with the 32CA reaction of nitrone 10 toward thioketone 11 in the gas phase and in the presence of THF is presented in Fig. 1.

Fig. 1 MPWB1K/6-311G(d) relative thermochemical parameters associated with the 32CA reaction between nitrone 10 and thioketone 11 in the gas phase and in the presence of THF. The blue and red colours denote meta and ortho regioisomeric channels, respectively. Nitrone10 + thioketone11, RPC, TS, and CA shown on the vertical lines indicate separate reagents, reactive pre-complex, transition state, and cycloadduct positions, respectively, along the reaction coordinate.

As shown in Fig. 1, the relative thermochemical parameters in the presence of THF are very similar to those found in the gas phase indicating neither kinetics nor thermodynamics of 32CA reaction between nitrone 10 and thioketone 11 can be affected by the inclusion of solvent effects; a characteristic which is expected for 32CA reactions. Moreover, relative Gibbs free energy profile manifestly demonstrates that the studied 32CA reaction in the presence of THF, although under some harsher conditions with respect to the gas phase, takes place through the regiospecific meta channel, ΔΔG_activation = 11.1 kcal mol⁻¹, affording CAm, ΔΔG_reaction = −16.1 kcal mol⁻¹, as the unique observable formal [3 + 2] cycloadduct. From these results it is quite clear that theoretical energetic outcomes not only are in excellent agreement with the experimental findings in the 32CA reaction of nitrone 6a with thioketone 8f (see Scheme 3) but the reasonability of reduced computational model is also verified.

The key geometrical parameters for the species involved in the studied 32CA reaction in both gas and THF phases are given in Table 2. Based on the geometrical parameters, the relative bond development index in a given TS, l_X−Y, is defined as follows:³⁴

where r^TS_X−Y and r^CA_X−Y denote the distance between two interacting centers X and Y in the TS and corresponding CA. Using bond distances given in Table 2, l_C1−S5 and l_O3−C4 become 0.585 and 0.490 Å, respectively, at TSm. Similarly, l_C1−C4 and l_O3−S5 are 0.603 and 0.572 Å, respectively, at TSoi. The degree of asynchronicity for a given TS can simply be measured via the difference between two l_X−Y and l_Z−W (Δl) values at such TS. The values of Δl are 0.095 Å at TSm and 0.031 Å at TSo implying that the more favourable TSm displays a more degree of asynchronicity than TSo in clear agreement with the lower imaginary frequency of TSm, 272.2i cm⁻¹, compared with that of TSo, 386.5i cm⁻¹.³⁵

Table 2 MPWB1K/6-311G(d) key geometrical parameters for the species involved in the 32CA reaction of nitrone 10 toward thioketone 11 in the gas phase and in the presence of THF (see Scheme 4 for atoms numbering)

	Structure	r (Å)
		C1–N2	N2–O3	C4–S5	C1–C4	O3–S5	C1–S5	O3–C4
Gas phase (ε = 1.00)	Nitrone10	1.293	1.233
	Thioketone11			1.614
	RPCm	1.289	1.240	1.620			3.720	3.036
	TSm	1.300	1.262	1.667			2.547	2.098
	CAm	1.458	1.408	1.849			1.800	1.390
	RPCo	1.294	1.230	1.613	3.438	3.514
	TSo	1.330	1.238	1.669	2.151	2.413
	CAo	1.458	1.400	1.811	1.540	1.690
THF (ε = 7.42)	Nitrone10	1.289	1.241
	Thioketone11			1.620
	RPCm	1.287	1.244	1.624			3.769	3.049
	TSm	1.296	1.268	1.676			2.587	2.030
	CAm	1.460	1.410	1.851			1.801	1.392
	RPCo	1.290	1.238	1.619	3.446	3.523
	TSo	1.333	1.234	1.679	2.090	2.483
	CAo	1.461	1.402	1.811	1.542	1.692

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Interestingly the degree of asynchronicity for TSm, Δl = 0.022 Å, becomes lower than that of TSo, Δl = 0.112 Å, when solvent effects of THF are taken into consideration indicating that while thermochemical parameters cannot significantly be affected by the inclusion of solvent, geometrical parameters are relatively more affected in the presence of solvent.

The electronic nature of the 32CA reaction between nitrone 10 and thioketone 11 was analysed by computing the global electron density transfer (GEDT)³⁶ at the corresponding TSs. In order to calculate the GEDT, the natural atomic charges at the TSs of the two regioisomeric channels, obtained through a natural population analysis (NPA), were shared between the nitrone and the thioketone frameworks. In gas phase, the GEDT that fluxes from the nitrone moiety toward the thioketone one is 0.06e at TSm and 0.12e at TSo. These very low GEDT values reveal that this 32CA reaction has a very low polar character.

3.2. DFT analysis based on the global and local reactivity indexes

Global reactivity indices defined within the conceptual DFT³⁷ are powerful tool to explain the reactivity and regioselectivity in the cycloaddition reactions. The global indexes, namely, electronic chemical potential (μ), chemical hardness (η), global electrophilicity (ω), and global nucleophilicity (N) for nitrone 10 and thioketone 11 are presented in Table 2.

As shown in Table 3, the higher electronic chemical potential of thioketone 11, −4.11 eV, than that of nitrone 10, −4.36 eV, predicts that along the corresponding 32CA reaction the GEDT will take place from thioketone 11 toward nitrone 10, in quite disagreement with the GEDT analysis performed on the corresponding TSs (see earlier). Nitrone 10 has a low global electrophilicity ω index, 1.27 eV, and a low nucleophilicity N index, 2.30 eV, being classified as marginal electrophile and a marginal nucleophile within the electrophilicity³⁸ and nucleophilicity³⁹ scales. On the other hand, thioketone 11 has a low global electrophilicity ω index, 1.41 eV, and a high nucleophilicity N index, 3.28 eV, being classified as a marginal electrophile and a strong nucleophile. Analysis of these global indices indicates that along a non-polar 32CA reaction, nitrone 10 and thioketone 11 will act as nucleophile and electrophile, respectively. The higher global electrophilicity index of thioketone 11 than that of nitrone 10 may be explained considering the presence of a highly polarizable sulfur atom in thioketone 11 which, despite of the presence a highly electron withdrawing CF₃ substitution in nitrone 10, acts as an electrophile. Consequently, in the case under study, the high polarization capability of C=S π electrons toward sulfur atom in thioketone 11 is preferred over the electron withdrawing character of CF₃ group in nitrone 10 allowing GEDT takes place from nitrone 10 toward thioketone 11. However, the moderate nucleophilic character of nitrone 10 and the moderate electrophilic character of thioketone 11 is responsible for a low polar character in the studied 32CA reaction.⁴⁰

Table 3 MPWB1K/6-311G(d) global electronic chemical potential, μ, global hardness, η, global electrophilicity, ω, and global nucleophilicity, N, in eV, for nitrone 10 and thioketone 11^a

	μ	η	ω	N*
a *εH(TCE) = −0.38209 a.u.
Nitrone 10	−4.36	7.47	1.27	2.30
Thioketone 11	−4.11	5.99	1.41	3.28

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When an electrophile–nucleophile pair is approached, the most favourable reactive channel is that associated with the initial two-centre interaction between the most electrophilic centre of electrophile and the most nucleophilic centre of nucleophile. Recently, Domingo have proposed the nucleophilic P_k⁻ and electrophilic P_k⁺ Parr functions³¹ derived from the excess of spin electron density reached via the GEDT process from the nucleophile to the electrophile as a powerful tool in the study of the local reactivity in polar processes. Since nitrone 10 and thioketone 11 act as nucleophile and electrophile, respectively, in the studied 32CA reaction; the nucleophilic P_k⁻ Parr functions of nitrone 10 and the electrophilic P_k⁺ Parr functions of thioketone 11 are calculated and depicted in Fig. 2.

Fig. 2 MPWB1K/6-311G(d) maps of Mulliken atomic spin density (ASD) of the radical cation nitrone 10˙⁺and nucleophilic P_k⁻ Parr function of nitrone 10; and ASD of the radical anion thioketone 11˙⁻and electrophilic P_k⁺ Parr function of thioketone 11.

As shown in Fig. 2, while the O3 oxygen atom in nitrone 10 is the most nucleophilic center possessing the maximum local nucleophilicity N_k of 1.65 eV, the most electrophilic center in thioketone 11 is the C4 carbon atom possessing the maximum local electrophilicity ω_k of 0.93 eV (atoms numbering is given in Scheme 4). Therefore, it is predicted that the most favourable electrophile–nucleophile interaction along the electrophilic attack of thioketone 11 on nitrone 10 should carry out between the most electrophilic center of thioketone 11, the C4 carbon atom, and the most nucleophilic center of nitrone 10, the O3 oxygen atom. This prediction is in complete agreement with the energetic study favouring meta regioisomeric channel in 32CA reaction between nitrone 10 and thioketone 11 as an investigated reduced computational model.

3.3. ELF topological analysis of the 32CA reaction between nitrone 10 and thioketone 11

The electron density, ρ(r), of a molecular system can represent all information hidden in the wave function of such system. Thus, a successive detection of the electron density changes along a chemical reaction in which a continuous redistribution of ρ(r) proceeds the reaction can provide valuable information about bonds forming/breaking patterns. In this way, from the molecular mechanistic point of view, our questions can greatly be addressed.⁴¹ One of the most popular function, introduce by Becke and Edgecombe,⁴² is electron localization function, ELF, by which essential information about the electron density shared between neighbouring atoms can be extracted.⁴¹

A great deal of work has confirmed that the ELF topological analysis of the bonding changes along a reaction path is a powerful tool to establish the molecular mechanism of a reaction.^43–45 After an analysis of the electron density, ELF provides basins which are the domains in which the probability of finding an electron pair is maximal. The basins are classified as core and valence basins. The latter are characterized by the synaptic order; i.e., the number of atomic valence shells in which they participate.⁴⁶ Thus, there are monosynaptic, disynaptic, trisynaptic basins and so on. Monosynaptic basins, labelled as V(A), correspond to lone pairs or non-bonding regions, while disynaptic basins, labelled as V(A,B), connect the core of two nuclei A and B and, thus, correspond to a bonding region between A and B. This description recovers the Lewis bonding model, providing a very suggestive graphical representation of the molecular system.

The ELF topological analysis of significant organic reactions involving the formation of new C–C single bonds has shown that it begins in the short C–C distance range of 1.9–2.0 Å by merging two monosynaptic basins, V(C_x) and V(C_y), into a new disynaptic basin V(C_x,C_y) associated with the formation of the new C_x–C_y single bond.⁴⁷ The C_x and C_y carbons characterized by the presence of the monosynaptic basins, V(C_x) and V(C_y), are called pseudoradical centres.⁴⁸

In order to understand the molecular mechanism of the 32CA reaction between nitrone 10 and thioketone 11, an ELF topological analysis of the MPWB1K/6-311G(d) wave functions of some relevant points, P1 through P12, was performed along the IRC profile associated with the more favourable TSm (see Fig. 3). While the attractor positions for the selected points within P1–P12 associated with the formation of CAm are shown in Fig. 4, the N populations of the most significant ELF valence basins at specific points along the IRC together with the atom numbering are displayed in Table 4. As shown in the first box in Fig. 4, labelled separate nitrone 10 and thioketone 11, the most relevant basins are those corresponding to the interacting systems on both nitrone 10 and thioketone 11; i.e., the C1–N2, N2–O3, and C4–S5 bonds. In nitrone 10, while the C1–N2 bonding region is characterized with the presence of V(C1,N2) disynaptic basin integrating 3.78e, the N2–O3 bonding region is characterized with the presence of V(N2,O3) disynaptic basin integrating 1.62e. Moreover, lone pairs of O3 are described with the presence of two V(O3) and V′(O3) monosynaptic basins with the sum population of 5.81e which is close to 6e. Consequently, C1–N2 and N2–O3 bonding region exhibit a double and single character, respectively, and O3 bears a one negative charge. The ELF valence shapes for nitrone 10 are in agreement with the corresponding Lewis structure presented in Scheme 4. Moreover, the C–S bonding region in thioketone 11 is identified with the existence of a V(C4,S5) disynaptic basin integrating 2.63e. Two V(S5) and V′(S5) monosynaptic basins over S5 atom in thioketone 11 each one with the population of 2.57e are related to S5 lone pairs. It is worthy to note that the significant decrease from the expected value of 4e found in the population of V(C4–S5) disynaptic basin, 2.63e, together with the noticeable increase from the expected value of 4e found in the sum of population of V(S5) and V′(S5) monosynaptic basins, 5.14e, clearly indicate the high polarization of π bonding electron density in C4–S5 double bond toward S5 in thioketone 11. Such behaviour makes a strong electrophilic character on C4 carbon atom in complete agreement with the discussion provided in section 3.2.

Fig. 3 MPWB1K/6-311G(d) IRC profile associated with the more favourable TSm of the studied 32CA reaction between nitrone 10 and thioketone 11 including the position of considered points P1–P12 in the ELF topological analysis.

Fig. 4 ELF attractor positions for the most relevant points associated with the formation of O3–C4 and C1–S5 single bonds along the 32CA reaction between nitrone 10 and thioketone 11.

Table 4 Valence basin populations N calculated from the ELF of some selected points, P1–P12, along the IRC curve associated with the more favourable TSm of 32CA reaction between nitrone 10 and thioketone 11

	Nitrone1	Thioketone2	P1	P2 (TSm)	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	CAm
d(O3–C4)/Å			2.824	2.098	2.029	1.914	1.778	1.760	1.733	1.707	1.689	1.647	1.631	1.508	1.391
d(C1–S5)/Å			3.222	2.547	2.496	2.414	2.321	2.309	2.290	2.270	2.257	2.224	2.210	2.074	1.800
GEDT(e)			0.02	0.06	0.04	0.00	−0.07	−0.09	−0.10	−0.12	−0.13	−0.16	−0.17	−0.28	−0.46
V(C1,N2)	3.78		3.69	3.96	3.16	2.57	2.35	2.33	2.30	2.26	2.25	2.20	2.19	2.04	1.81
V′(C1,N2)
V(N2)					0.88	1.28	1.62	1.65	1.71	1.76	1.79	1.85	1.88	2.06	2.34
V(N2,O3)	1.62		1.58	1.39	1.35	1.27	1.19	1.18	1.16	1.15	1.15	1.13	1.11	1.05	1.01
V(O3)	2.83		2.96	2.92	2.91	2.86	2.77	2.76	2.74	2.69	2.68	2.64	2.64	2.54	2.41
V′(O3)	2.98		2.89	2.87	2.88	2.92	3.22	3.25	3.27	2.64	2.62	2.59	2.58	2.52	2.49
V′′(O3)										0.71	0.75
V(C1)						0.38	0.47	0.48	0.50	0.53	0.54	0.57	0.58
V(C4,S5)		2.63	2.55	2.34	2.31	2.26	2.02	2.00	1.98	1.95	1.93	1.89	1.88	1.78	1.61
V′(C4,S5)
V(C4)
V(S5)		2.57	2.60	2.63	2.63	2.62	2.58	2.87	2.56	2.90	2.90	2.51	2.50	2.41	2.28
V′(S5)		2.57	2.59	2.74	2.76	2.80	2.86	2.57	2.88	2.54	2.53	2.57	2.54	2.42	2.28
V′′(S5)												0.35	0.38
V(C1,S5)														1.25	1.69
V(O3,C4)												0.86	0.90	1.14	1.39

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At P1, d(O3–C4) = 2.824 Å and d(C1–S5) = 3.222 Å, reagents are too far apart and the ELF valence basin patterns, as presented in Fig. 4, are similar to those found for separate regents except some slight changes in their populations shown in Table 4. At P2, d(O3–C4) = 2.098 Å and d(C1–S5) = 2.547 Å, which is associated with the favourable TSm of the studied 32CA reaction, no significant changes happen in the ELF valence shapes compared with P1. At this point, while slight changes occur in the valence ELF populations, the maximum GEDT of 0.06 is reached from nitrone fragment toward thioketone one. At P3 where d(O3–C4) = 2.029 Å and d(C1–S5) = 2.496 Å, emerging a new V(N2) monosynaptic basin corresponded to N2 lone pair with an initial population of 0.88e is the unique notable happening among ELF valence basin patterns. In addition, the GEDT value reduces to 0.04e. At P4 characterized with d(O3–C4) = 1.914 Å and d(C1–S5) = 2.414 Å while the GEDT balances between two fragments, a new V(C1) monosynaptic basin integrating 0.38e emerges over C1. Indeed, the presence of highly electron withdrawing CF3 group on C1 carbon atom not only balances the GEDT between two fragments but also allows a pseudoradical center is stabilized and formed over C1 in a very early point compared with point P12 where C1–S5 single bond begins to form. Interestingly, from P5 to final cycloadduct CAm, GEDT takes place in a reverse direction from thioketone moiety toward nitrone one. As two fragments become closer along points P4 through P8 while no notable changes happen in the ELF valence shapes, in addition to some changes in the ELF valence populations the value of GEDT successively increases as well. At P8, d(O3–C4) = 1.707 Å and d(C1–S5) = 2.270 Å, a new V′′(O3) monosynaptic basin with an initial population of 0.71e creates over O3 oxygen atom as a direct consequence of a sudden depopulation of V′(O3) monosynaptic basin from 3.27e at P7 to 2.69e at P8. As reaction proceeds, at P9 for which d(O3–C4) and d(C1–S5) are, respectively, 1.689 and 2.257 Å while V′′(O3) monosynaptic basin emerged at P8 increases its population to 0.75e, no significant change in the ELF valence basin shapes is observed. At P10, d(O3–C4) = 1.647 Å and d(C1–S5) = 2.224 Å, coincided with disappearing V′′(O3) monosynaptic basin and creation of a new V(O3,C4) disynaptic basin integrating 0.86e, a new V′′(S5) monosynaptic basin emerges over S5 with an initial population of 0.35e. Therefore, while at P10 formation of O3–C4 single bond beings, a sudden depopulation of V(S5) monosynaptic basin from its maximum value of 2.90e at P9 to 2.51e at P10 leads to creation of pseudoradical center over S5. Consequently at P10 the two pseudoradical centers required for the subsequent C1–S5 single bond formation are already formed. At P11 the ELF valence basin patterns do not experience any notable changes except slight tolerance in their populations. Finally, at P12 in which d(O3–C4) and d(C1–S5) are 1.508 and 2.074 Å, respectively, the more delayed C1–S5 single bond begins to form via C-to-S coupling of the two pseudoradical C1 and S5 centers. The formation of C1–S5 single bond takes place by merging of two V(C1), created at very early point P4, and V′′(S5), appeared at the very late point P10, monosynaptic basins into a new V(C1,S5) disynaptic one integrating 1.25e. The ELF topological analysis of the studied 32CA reaction clarifies that while formation of C1–S5 single bond is a direct consequence of participation both pseudoradical C1 and S5 centers, formation of O3–C4 one is a result of sharing electron density from one of O3 oxygen lone pairs toward C4 carbon atom. Indeed, as depicted in Fig. 4 and presented in Table 4, there is not any V(C4) monosynaptic basin along the IRC curve of the 32CA reaction between nitrone 10 and thioketone 11. The lack of presence V(C4) monosynaptic basin can be attributed to the high polarization of C4–S5 double bond toward highly polarizable S5 sulfur atom. As mentioned, from point P4 and thereafter GEDT takes place from thioketone fragment toward the nitrone one. Therefore, polarization of C4–S5 single bond extremely increases toward S5 (the C–S double bond is mainly depopulated over S5 rather than C4) and, thus, C4 is not allowed to behave as a pseudoradical center generating a monosynaptic basin. Basin-population changes which are collected in Table 4 can graphically be summarized in Fig. 5.

Fig. 5 Graphical representation of the basin-population changes along the more favourable meta regioisomeric channel of 32CA reaction between nitrone 10 and thioketone 11.

Considering Fig. 5, some appealing conclusions can be summarized as follows:

• Basin-population changes can mainly be divided into three different regions; P1–P5, P5–P8, and P8–P12 regions;

• At the first region, P1 through P5, while V(N2,O3) population experiences a slight downward slope, V(O3) population remains almost unchanged. On the other hand a severe downward slope is observed in the V(C1,N2) population indicating depopulation of V(C1,N2) mainly toward C1 leading to form V(C1) and V(N2) monosynaptic basins. Since the formation of V(N2) monosynaptic basin at P3 is prior to V(C1) one at P4, the V(N2) population mainly comes from the slight depopulation of V(N2,O3) within P1 to P3. The main part of V(N2,O3) population is gathered over O3 atom at P4 where the V′(O3) population begins to increase with a steep upward slope. Moreover, both notable downward changes in V(C4,S5) during P1 to P2 and P4 through P5 are mainly attributed to depopulation of V(C4,S5) toward highly polarizable S5 sulfur atom leading to a significant increase in the V′(S5) population. It is interesting to note that at P4, due to presence of highly electron withdrawing CF₃ group on nitrone fragment, not only GEDT is balanced between two fragments, but also a pseudoradical center characterized with V(C1) is allowed to be stabilized and formed in a very early region;

• At the second region, P5 through P8, in which a reverse direction can clearly be detected for GEDT, a sinusoidal alternating pattern is observed in the V(S5) and V′(S5) population changes. Such sinusoidal pattern may be related to the fluctuations in the electron density of S5 lone pairs from which GEDT takes place toward nitrone moiety and, on the other hand, S5 should get ready to generate a pseudoradical center in the next region. Additionally, V′(O3) monosynaptic basin reaches to its maximum population at P7. On going from P7 to P8, a sudden and severe decrease in V′(O3) population leads to creation a V′′(O3) monosynaptic basin at P8. Meanwhile, along P7 to P8 the V(S5) population begins to increase;

• Finally, at third region, P8–P12, coincided with the shift of GEDT toward more negative values, the O3–C4 single bond which is characterized by the appearance of V(O3,C4) disynaptic basin begins to form at a very short distance of 1.647 Å at P10. Interestingly, the electron density required for O3–C4 single bond formation is provided by one of V(O3) monosynaptic basins, specifically V′(O3), associated with the lone pairs of the nitrone O3 oxygen atom. Furthermore, formation of O3–C4 single bond is accompanied with the creation of V′′(S5) monosynaptic basin as a direct consequence of a significant depopulation of V(S) between P9 and P10. At P12, formation of C1–S5 single bond, identified with the presence of V(C1,S5) disynaptic basin, starts at a distance of 2.074 Å. It is worth noting that unlike the pattern observed for O3–C4 single bond formation, formation of C1–S5 single bond follows the recently proposed pattern.^49,50 In fact, depopulation of C4=S5 and C1=N2 double bonds followed by the formation of two non-bonding V(C1) and V(S5) monosynaptic basins and, then, merging of two aforementioned monosynaptic basins into one V(C1,S5) disynaptic basin portray details of C1–S5 single bond formation.

The ELF analysis performed on the reduced computational model evidences that formation of C–O and C–S single bonds takes place via a non-concerted one-step mechanism rejecting the pericyclic mechanism for cycloaddition reactions in which a concerted movement is considered for electrons.⁵¹

4. Conclusion

The 32CA reaction of fluorinated nitrone 6a toward thioketone 8f in the presence of THF, experimentally studied by Mlostoń and co-workers, was theoretically modelled using fluorinated nitrone 10 and thioketone 11 at the MPWB1K/6-311G(d) level. The energetic study of reaction paths involved in the computationally modelled reaction obviously showed that 32CA reaction between nitrone 10 and thioketone 11, in the gas phase as well as in the presence of THF, carries out via the extremely regioselective (regiospecific) meta channel furnishing CAm as the unique kinetically and thermodynamically observable cycloadduct. These results which are in excellent agreement with the experimental findings for 32CA reaction of nitrone 6a toward thioketone 8f confirm the reasonability of investigated reduced computational model.

Despite the presence of highly electron withdrawing CF₃ substitution in nitrone 10, the presence of highly polarizable sulfur atom in thioketone 11 makes it possible nitrone 10 acts as a nucleophile in the presence of thioketone 11. Analysis of the global DFT reactivity indices indicates that the moderate nucleophilic character of nitrone 10 and the moderate electrophilic character of thioketone 11 is responsible for a low polar character in the studied 32CA reaction presenting a very low GEDT value of 0.06 in more favourable TSm.

The complete regioselectivity in the modelled 32CA reaction, in quite agreement with experimental outcome, can be explained using calculated electrophilic and nucleophilic Parr functions at the interacting sites of reagents. Indeed, the most electrophilic activation found at the C4 carbon atom of thioketone 11, possessing the maximum local electrophilicity ω_k of 0.93 eV and the most nucleophilic activation found at the O3 oxygen atom of nitrone 10, possessing the maximum local nucleophilicity N_k of 1.65 eV, initializes corresponding 32CA reaction via electrophilic attack of thioketone 11 on nitrone 10.

The ELF analysis performed on the computationally modelled 32CA reaction clarified interesting points about the molecular mechanism of this reaction in which carbon–heteroatoms interactions lead to generate corresponding cycloadduct. In this relation, while the C1–S5 single bond formation at a distance of 2.074 Å takes place exactly according to the Domingo's proposed pattern,^49,50 formation of O3–C4 single bond at a very short distance of 1.647 Å follows a quite different pattern. In other word, depopulation of C4=S5 and C1=N2 double bonds followed by the formation of two non-bonding V(C1) and V(S5) monosynaptic basins and, then, merging of two aforementioned monosynaptic basins into one V(C1,S5) disynaptic basin portray the mechanism of C1–S4 single bond formation. On the other hand, the O3–C4 single bond formation occurs through a direct participation of electron density from one of O3 lone pairs in nitrone fragments which is shared toward electrophilically activated C4 carbon atom in thioketone fragment. The patterns obtained via ELF topological analysis authoritatively allow to reject the pericyclic mechanism for cycloaddition reactions in which a concerted movement is suggested for electrons.⁵¹

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